Multi-agent language systems are often deployed under the assumption that collaboration improves reasoning quality, but this assumption breaks down once token cost, latency, and collaboration-induced errors enter the picture. We study protocol selection under a cost-aware utility objective, where the system decides on each input whether to run a collaborative protocol or fall back to solo reasoning. We propose Causal Advantage Routing for Language agents (CARL), a contextual-bandit framework that estimates the conditional collaboration advantage of each protocol over solo reasoning. CARL combines confounded execution logs with budgeted randomized probes, forms one-vs-solo doubly robust scores and shrunken DR-derived pseudo-outcomes, and at deployment uses a one-sided predictive lower bound for a future realized protocol-solo contrast, otherwise abstaining to solo execution. Across math, code, and multi-hop question-answering benchmarks with an open-weight model, CARL improves cost-aware utility and substantially reduces harmful collaboration over fixed protocols, compute-matched solo strategies, MAS routers, cascade methods, and causal routing baselines, indicating that effective multi-agent systems should estimate when collaboration is causally worth its cost rather than invoking it by default.